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Ocean eddies affect large‐scale circulation and induce a kinetic energy cascade through their non‐linear interactions. However, since global observations of eddy dynamics come from satellite altimetry maps that smooth eddies and distort their geometry, the strength of this cascade is underestimated. Here, we use deep learning to improve observational estimates of global surface geostrophic currents and explore the implications for the cascade. By synthesizing multi‐modal satellite observations of sea surface height (SSH) and temperature, we achieve up to a 30% improvement in spatial resolution over the community‐standard SSH product. This reveals numerous strongly interacting eddies that were previously obscured by smoothing. In many regions, these newly resolved eddies lead to nearly an order‐of‐magnitude increase in the upscale kinetic energy cascade that peaks in spring and is strong enough to drive the seasonality of large mesoscale eddies. Our study suggests that deep learning can be a powerful paradigm for satellite oceanography. Plain Language Summary: We developed a deep learning method to estimate global maps of surface ocean currents from satellite observations with significantly improved resolution and accuracy compared to existing methods. These maps dramatically improve our ability to observe eddy dynamics and the impact of eddies on the transfer of energy between scales in the ocean. Our study suggests that deep learning can be a powerful paradigm for satellite oceanography. Key Points: We develop the first deep learning global estimates of surface ocean currents from multi‐modal satellite observationsOur deep learning method is able to map surface currents with state‐of‐the‐art resolution and accuracyThe diagnosed kinetic energy cascade is an order of magnitude higher compared to conventional altimetry products [ABSTRACT FROM AUTHOR]

Eddies of various sizes are visible to the naked eye in turbulent flow. Each eddy scale corresponds to a fraction of the total energy released by the turbulence cascade. Understanding the dynamic mechanism of the energy cascade is crucial to the study of turbulent mixing. In this paper, an energy cascade multi-layer network (ECMN) based on the complex network algorithm is proposed to investigate the spatio-temporal evolution of the energy cascade, covering both the inertial and dispersive ranges. The dynamic process of energy cascade is transformed into a topological structure based on the node definition and edge determination. The topological structure allows for the exploration of eddies interaction and chaotic energy transfer across scales. The model results show the intermittent and non-uniform nature of the energy cascade. Meanwhile, the scale gap found in the model verifies the fractal property of the energy evolution. We also found that scales of the generated eddies in energy cascade process are stochastic, and a synchronous energy cascade pattern is demonstrated according to the constructed framework. Furthermore, it provides a topological way to evaluate the contribution of large and small scale eddies. In addition, a network structure coefficient κ is proposed to evaluate the energy transfer strength. It agrees very well with the fluctuation of dissipation rates. All of this shows that the network model can effectively reveal the inhomogeneous properties of the energy cascade and quantify the turbulent mixing intensity based on the intermittent scale interaction. This also provides new insights into the study of fractal scales of nonlinear complex systems and the bridging of chaotic dynamics with topological frameworks. [ABSTRACT FROM AUTHOR]

Lewis Fry Richardson proposed his famous picture of turbulent flows in 1922, where the kinetic energy is transferred from large-scale to small-scale structures until the viscosity converts it into heat. This cascade idea, also known as the forward energy cascade, is now widely accepted and is treated as the cornerstone of not only turbulent modeling, but also global circulation models of the ocean and atmosphere. In this work, the Filter-Space-Technique is applied to the oceanic flow field provided by the CMEMS reanalysis model to quantify the scale-to-scale energy flux. A rich dynamical pattern associated with different scales is observed. More precisely, either positive or negative fluxes are observed, indicating the direction of the energy cascade, where the energy is transferred from large-scale structures to small-scale ones or vice versa. High-intensity energy exchange is found mainly in the Western Boundary Current Systems and Equatorial Counter Currents. For the latter case, a wavelike pattern is observed on the westward travel. Moreover, strong seasonal variation is evident for some scales and regions. These results confirm the existence of forward and inverse cascades and rich regional dynamics. [ABSTRACT FROM AUTHOR]

Understanding and predicting turbulent flow phenomena remain a challenge for both theory and applications. The nonlinear and nonlocal character of small-scale turbulence can be comprehensively described in terms of the velocity gradients, which determine fundamental quantities like dissipation, enstrophy, and the small-scale topology of turbulence. The dynamical equation for the velocity gradient succinctly encapsulates the nonlinear physics of turbulence; it offers an intuitive description of a host of turbulence phenomena and enables establishing connections between turbulent dynamics, statistics, and flow structure. The consideration of filtered velocity gradients enriches this view to express the multiscale aspects of nonlinearity and flow structure in a formulation directly applicable to large-eddy simulations. Driven by theoretical advances together with growing computational and experimental capabilities, recent activities in this area have elucidated key aspects of turbulence physics and advanced modeling capabilities. [ABSTRACT FROM AUTHOR]

The geometrically complex mechanisms of energy transfer in the compound space of scales and positions of wall turbulent flows are investigated in a temporally evolving boundary layer. The phenomena consist of spatially ascending reverse and forward cascades from the small production scales of the buffer layer to the small dissipative scales distributed among the entire boundary layer height. The observed qualitative behaviour conforms with previous results in turbulent channel flow, thus suggesting that the observed phenomenology is a robust statistical feature of wall turbulence in general. An interesting feature is the behaviour of energy transfer at the turbulent/non-turbulent interface, where forward energy cascade is found to be almost absent. In particular, the turbulent core is found to sustain a variety of large-scale wall-parallel motions at the turbulent interface through weak but persistent reverse energy cascades. This behaviour conforms with previous results in free shear flows, thus suggesting that the observed phenomenology is a robust statistical feature of turbulent shear flows featuring turbulent/non-turbulent interfaces in general. [ABSTRACT FROM AUTHOR]

We study analytically the dynamics of a $ d $-dimensional Klein-Gordon lattice with periodic boundary conditions, for $ d \leq 3 $. We consider initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation, the resonant normal form of the system is given by a small-dispersion nonlinear Schrödinger (NLS) equation. By exploiting a result about the growth of Sobolev norms for solutions of the small-dispersion NLS equation, we are able to describe an energy cascade phenomenon for the Klein-Gordon lattice, where part of the energy is transferred to modes associated to higher frequencies. Such a phenomenon holds within the time-scale for which we can ensure the validity of the continuous approximation. [ABSTRACT FROM AUTHOR]

As the key scale and important link of material cycle, energy cascade and information transmission, ocean mesoscale eddy (OME) has rich thermodynamic connotation. Based on the kinetic energy zoning of OME in China seas and the adjacencies (CSA), this paper mainly summarized the motion properties, dynamic essence and local characteristics of the OME in the CSA, and elaborated generation, propagation and energy cascade dissipation of OME disturbances, as well as the impaction of the OME in the processes of ocean current dynamics, heat and salt allocation, biogenic elements cycle and mesoscale sea-air interaction from the perspective of scale limitation and association, and subsequently put forward research suggestions on relevant scientific issues and progress. The results showed that the evolution and dynamics of the OME was of great significance for understanding the multi-dimensional levels, scale-quantity and process-forms of the material and energy transmission in the ocean. It was necessary to comprehensively deepen the research on the self-adaptive observation and the predictability of OME, enhance the studies on scale deduction and specificity, establish an energy information channel from the weather scale to the climatic, environmental, ecological impaction and disaster risk, and build the theory and model of mesoscopic ecosystem dynamics. We should explore new ways, from the viewpoint of the OME, to refine disaster risk projection, zoning and security governance.

A linear dynamical model for the development of the turbulent energy cascade was introduced in Apolinário et al. (J. Stat. Phys., 186, 15 (2022)). This partial differential equation, randomly stirred by a forcing term which is smooth in space and delta-correlated in time, was shown to converge at infinite time towards a state of finite variance, without the aid of viscosity. Furthermore, the spatial profile of its solution gets rough, with the same regularity as a fractional Gaussian field. We here focus on the temporal behavior and derive explicit asymptotic predictions for the correlation function in time of this solution and observe that their regularity is not influenced by the spatial regularity of the problem, only by the correlation in time of the stirring contribution. We also show that the correlation in time of the solution depends on the position, contrary to its correlation in space at fixed times. We then investigate the influence of a forcing which is correlated in time on the spatial and time statistics of this equation. In this situation, while for small correlation times the homogeneous spatial statistics of the white-in-time case are recovered, for large correlation times homogeneity is broken, and a concentration around the origin of the system is observed in the velocity profiles. In other words, this fractional velocity field is a representation in one-dimension, through a linear dynamical model, of the self-similar velocity fields proposed by Kolmogorov in 1941, but only at fixed times, for a delta-correlated forcing, in which case the spatial statistics is homogeneous and rough, as expected of a turbulent velocity field. The regularity in time of turbulence, however, is not captured by this model.

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We study a binary tree-structured multi-degree-of-freedom nonlinear oscillator with impulsive and continuous excitations. The response of this model is studied for excitations that are applied to the largest masses. It is shown how choosing the mass of the smallest blocks influences the response of the system regarding the dissipation and how efficient targeted energy transfer is realized in the system. The simplified frequency energy plot is introduced as a means of analyzing the response of multi-degree-of-freedom systems for impulsive excitations. For continuous excitations, it is shown that the smallest masses (nonlinear energy sinks) are active only inside specific nonlinear frequency bands when the excitation amplitude is sufficiently high. [ABSTRACT FROM AUTHOR]

We construct a three-dimensional vector field that exhibits positive energy flux at every Littlewood–Paley shell and has the best possible regularity in L p -based spaces, p ≤ 3 ; in particular, it belongs to H (5 6) - . [ABSTRACT FROM AUTHOR]

Submesoscale oceanic structures (

The ocean behaves as a typical multiscale fractal structure, whose dynamic and thermal variabilities extend over a wide range of spatial scales, r, spanning from 10−3 to 107 m. Studying the statistical characteristics of multiscale fractal structures is crucial to understanding the interactions and energy cascade processes between different spatial scales. Remote sensing data are one of the best choices for revealing these statistical characteristics. This work analyzes the multiscale (1–1000 km) fractal structures of sea surface temperature (SST) from the Level-2+ (L2P) satellite orbit Visible Infrared Imaging Radiometer Suite (VIIRS) products over the Kuroshio Extension (KE) region (145°E–160°W, 20°N–50°N), using a conventional method (second-order structure function, D(r)) and a newly developed statistical method (spatial variance, V(r)). The results show that both the power-law distribution slopes of D(r) and V(r) are close to 2/3, which is equivalent to the −5/3 wavenumber spectrum. V(r) is found to be more robust when depicting the fractal structure and variance density, V'(r), compared with D(r). V'(r) is slightly larger at the mesoscale (50–150 km) than at the large scale (higher than 150 km) and is much smaller than that at the submesoscale (smaller than 50 km). Additionally, V'(r) has an indiscernible diurnal variation but remarkable seasonal and latitudinal variations. For the seasonal variability, the maximum V'(r) appears in winter at the large scale and mesoscale, and gradually shifts towards spring at the submesoscale, which implies that a forward energy cascade process may occur during this period. The maximum of the latitude-dependent V'(r) appears around 40°N for all the scales. It is consistent with the latitude of the strongest background SST gradient, indicating that the background SST front is the main source of the strong SST multiscale spatial variabilities over the KE region. This work benefits the application of other high-resolution remote sensing data in this research field, including the forthcoming Surface Water Ocean Topography (SWOT) satellite product. [ABSTRACT FROM AUTHOR]

Lake sturgeon (Acipenser fulvescens) have recently been a target for conservation in the Laurentian Great Lakes. While improving spawning success has been a major goal of these efforts, an often-overlooked component is the survival of the larvae after hatching, during the period of downstream drift. In a dammed river system, during this phase, larvae may need to drift past dam infrastructure. This journey past dams often results in an increase in larval mortality for a variety of reasons, including exposure to highly turbulent flow. Quantifying the aspects of turbulence related to larval mortality within fishways will inform retrofitting or future design efforts of fishways to improve larval viability. This study uses dimensional arguments to characterize the flow conditions influencing larval viability through fishways. One such condition discussed here is strain rate, which can be used as a diagnostic basis to determine candidate fishways for conservation measures. Based on Kolmogorov's theory (1941), the strain rate present in the fishway at the pertinent scale for lake sturgeon larvae, S η , can be estimated using the fishway's macroscale Reynolds number Re , the relevant macroscale fishway velocity U , and the smallest fishway pool dimension l e as S η l e /U ≈ Re 1/2. This approach is illustrated in the case of the Vianney-Legendre Fishway in Québec, and determined this fishway to be potentially hazardous to drifting lake sturgeon larvae. [ABSTRACT FROM AUTHOR]

We present large eddy simulations of a midlatitude open ocean front using a modified state-of-the-art computational fluid dynamics code. We investigate the energy and information fluxes at the submesoscale/small-scale range in the absence of any atmospheric forcing. We find submesoscale conditions ( R o ∼1, R i ∼1) near the surface within baroclinic structures, related to partially imbalanced frontogenetic activity. Near the surface, the simulations show a significant scale coupling on scales larger than ∼ 10 3 (m). This is manifested as a strong direct energy cascade and intense mutual communication between scales, where the latter is evaluated using an estimator based on Mutual Information Theory. At scales smaller than ∼ 10 3 (m), the results show near-zero energy flux; however, at this scale range, the estimator of mutual communication still shows values corresponding with a significant level of communication between them. This fact motivates investigation into the nature of the self-organized turbulent motion at this scale range with weak energetic coupling but where communication between scales is still significant and to inquire into the existence of synchronization or functional relationships between scales, with emphasis on the eventual underlying nonlocal processes. [ABSTRACT FROM AUTHOR]

Using the local multiscale energy and vorticity analysis (MS-EVA) and based on the global high-resolution ocean reanalysis product GLORYS12V1 for 20 years, this study investigates the energy transfers and conversions of Kuroshio in the Luzon Strait and its adjacent regions through three scales, namely, the climatological scale, the seasonal scale, and the eddy scale. The results show that the inverse cascades of kinetic energy dominate the energy transfer east of Luzon (at both the eddy and seasonal scales). Kuroshio transfers the climatological kinetic energy to the eddy scale through a forward energy cascade in Luzon Strait and east of Taiwan. Because the topography of Luzon Strait and Kuroshio jointly block and limit the westward propagation of non-local eddies, the eddy energy in the South China Sea west of Luzon Strait tends to depend on local forward potential energy cascades. In these subregions, potential energy drives the accumulation of kinetic energy under the action of buoyancy conversion: interannual (seasonal) potential energy as the source of multiscale energy in the Luzon Strait (the east of Taiwan). [ABSTRACT FROM AUTHOR]

Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2022 Nonlinearity35, 1380-1401), we reformulated the energy cascade in terms of this stretching process and derived the −5/3 law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'. [ABSTRACT FROM AUTHOR]

Breaking internal tides and induced mixing are critical to shelf dynamics, including heat and mass exchanges. Spatiotemporal variability of internal tides and modulation factors for the southern East China Sea shelf were examined based on a combination of a three-month mooring velocity and satellite altimeter data. Semidiurnal and diurnal internal tides exhibited distinct temporal trends, with the semidiurnal internal tides enhanced by an order of magnitude during the latter half of the record, while the diurnal internal tides followed quasi spring-neap cycles with a generally stable intensity except for two specific periods of strengthening. These internal tides probably originated remotely over the shelf-slope area northeast of Taiwan. Time-varying stratification was the most important factor for the internal tidal magnitude. In addition, varying background currents influenced the diurnal critical latitude band, which explains the slightly enhanced diurnal internal tides during the two periods. Although both semidiurnal and diurnal internal tides were mode-1 dominated, the semidiurnal internal tides were surface intensified while the diurnal tides were bottom intensified. The proportion of higher mode internal tides increased during robust eddy activities. Stronger background vertical shear corresponded to high-frequency events and energy transfers from tidal frequencies to high frequencies associated with turbulent mixing. [ABSTRACT FROM AUTHOR]

Tidal currents are predominant in coastal areas, causing the generation of vortices at different scales. We reproduce the main process of vortex shedding generated in tidal systems with inlets and channels using a laboratory large‐scale model. A filter‐space technique is implemented to analyze nonlinear energy/enstrophy transfer rates and map out the energy pathways through the flow scales of the measured velocity fields. We provide sound evidence of the transitional character of the energy cascades during a tidal period. The periodic generation and destruction of tidal vortices plays a relevant role in the transition from an inverse to a direct energy cascade within a tidal period. The period‐averaged energy budget shows the coexistence of multiple cascades. Small scales follow a direct energy cascade, whereas a split‐energy cascade is found at intermediate and large scales, where part of the injected energy goes to small scales and part to a larger flow scale. Plain Language Summary: Remote sensing images from a satellite of ocean and coastal areas offer unique opportunities to observe vortical flow structures. Coastal areas are often dominated by tidal currents that interact with coastline features (island, headlands or capes, and inlets) and periodically shed vortices at different scales. Coastal vortices are known to play a fundamental role in momentum, mass, and energy transport. Understanding how energy is exchanged among the wide range of flow scales (small/large vortices and large‐scale tidal circulations) is a fundamental question that deserves a thorough investigation, owing to the great impact on the coastal dynamics. With this in mind, we used a large‐scale physical model to accurately recreate the main processes that lead to the generation of tidal vortices observed around natural inlets. The measured velocity fields have been analyzed with filtering techniques that allow for understanding the direction of energy exchanges. We demonstrated that the periodicity of the tidal flow produces multiple energy cascades depending on the tidal phase. We found that energy followed dual pathways toward large scales and vice versa. Key Points: We recreate the generation of tidal vortices at different scales around tidal inlets using a laboratory modelVortices shed around the inlet undergo a merging‐thinning process leading to macro flow gyres that occupy the entire tidal flatsThe results of filter‐space analysis demonstrate the coexistence of energy and enstrophy multiple cascades depending on the tidal phase [ABSTRACT FROM AUTHOR]

We study two dyadic models for incompressible ideal magnetohydrodynamics, one with a uni-directional energy cascade and the other one with both forward and backward energy cascades. Global existence of weak solutions and local well-posedness are established for both models. In addition, solutions to the model with uni-directional energy cascade associated with positive initial data are shown to develop blow-up at a finite time. Moreover, a set of fixed points is found for each model. Linear instability about some particular fixed points is proved. [ABSTRACT FROM AUTHOR]

Spatial‐temporal submesoscale variabilities in the upper Red Sea and their generation mechanisms, including frontogenesis, mixed‐layer instability (MLI), and symmetric instability (SI) are qualitatively investigated using high‐resolution simulations. The results suggest that submesoscales are critical hydrodynamic components and stirring at submesoscale has a clear signal in the Red Sea, enhanced in winter, particularly in the central and northern basins, and intensified toward the eastern coast. Frontogenesis and MLI energize submesoscales with winter peaks, when SI could also be triggered by the enhanced frontal gradients and buoyancy loss that reduce the surface potential vorticity. The MLI and SI have larger (smaller) scales in winter (summer). The seasonal submesoscale variability is governed by the vertical structure of the mixed layer forced by atmospheric conditions, significantly modulating the mesoscale eddies' seasonality via an inverse cascade. This study offers new insights into understanding the Red Sea submesoscales and have potential applications to other marginal seas. Plain Language Summary: Oceanic submesoscale dynamics have small dimensions (1–10s km), and they are important in the variability of physical, biological and chemical processes. We used a high‐resolution numerical model to study the spatial‐temporal submesoscale variabilities in the upper Red Sea, as well as their driving force and energy budget. We found that submesoscales are critical components in the Red Sea dynamics and make important contributions to stirring and transport in the basin. The seasonal submesoscale variability is essentially driven by atmospheric conditions and can modulate the eddiesʼ seasonality by converting energy from smaller scales to larger scales. This study offers new insights into understanding the Red Sea submesoscales and has potential applications to other marginal seas in the global oceans. Key Points: The Red Sea submesoscales are enhanced in winter and enhanced toward the northern and eastern basin due to buoyancy flux and Ekman effectsSubmesoscales are forced by seasonal atmospheric conditions and modulate the seasonality of the mesoscales via an inverse energy cascadeSubmesoscales may play a role in chaotic stirring in the Red Sea, although they are dominated by two‐dimensional structures [ABSTRACT FROM AUTHOR]

Magnetic flux ropes (MFRs)—transient magnetic structures widely observed in Earth's magnetosphere—play crucial roles in particle acceleration and energy dissipation. MFRs above ion scale have been well studied, while MFRs at subion scales and their coupling with larger‐scale ropes still remains not well understood. In this paper, we present the first observation of a subion‐scale MFR nested in an ion‐scale MFR, using high‐resolution data from the magnetospheric multiscale (MMS) mission. We find that the subion‐scale MFR hosts more intense plasma activity than the ion‐scale MFR, including distinct electron agyrotropy and strong electromagnetic turbulence. In addition, axis of the subion‐scale MFR is oblique to that of the ion‐scale MFR, indicating that their generation may be ascribed to 3D magnetic reconnection. Observations of such cross‐scale structure may shed new lights into understanding energy cascade in space plasmas. Plain Language Summary: In this study, we report the first observation of a subion‐scale flux rope nested in an ion‐scale flux rope in Earth's magnetotail and resolve their dynamics and properties in great detail by using high‐cadence data from the MMS mission. We find that the two ropes have different properties, for instance, the smaller‐scale rope hosts stronger plasma activity. This study can improve our understanding of cross‐scale coupling of the magnetic flux ropes and energy cascade in space plasmas. Key Points: A subion‐scale flux rope nested in an ion‐scale flux rope is reported for the first timeThe subion‐scale rope hosts more intense waves than the ion‐scale rope doesSuch cross‐scale structure may result from 3D magnetic reconnection and play a crucial role in energy cascade in space plasmas [ABSTRACT FROM AUTHOR]

We present large eddy simulations of a midlatitude open ocean front using a modified state-of-the-art computational fluid dynamics code. We investigate the energy and information fluxes at the submesoscale/small-scale range in the absence of any atmospheric forcing. We find submesoscale conditions (Ro∼1, Ri∼1) near the surface within baroclinic structures, related to partially imbalanced frontogenetic activity. Near the surface, the simulations show a significant scale coupling on scales larger than ∼103 (m). This is manifested as a strong direct energy cascade and intense mutual communication between scales, where the latter is evaluated using an estimator based on Mutual Information Theory. At scales smaller than ∼103 (m), the results show near-zero energy flux; however, at this scale range, the estimator of mutual communication still shows values corresponding with a significant level of communication between them. This fact motivates investigation into the nature of the self-organized turbulent motion at this scale range with weak energetic coupling but where communication between scales is still significant and to inquire into the existence of synchronization or functional relationships between scales, with emphasis on the eventual underlying nonlocal processes.

A new local kinetic energy (KE) budget for the Madden-Julian Oscillation (MJO) is constructed in a multi-scale framework. This energy budget framework allows us to analyze the local energy conversion processes of the MJO with the high-frequency disturbances and the low-frequency background state. The KE budget analysis is applied to a pronounced MJO event during the DYNAMO field campaign to investigate the KE transport path of the MJO. The work done by the pressure gradient force and the conversion of available potential energy at the MJO scale are the two dominant processes that affect the MJO KE tendency. The MJO winds transport MJO KE into the MJO convection region in the lower troposphere while it is transported away from the MJO convection region in the upper troposphere. The energy cascade process is relatively weak, but the interaction between high-frequency disturbances and the MJO plays an important role in maintaining the high-frequency disturbances within the MJO convection. The MJO KE mainly converts to interaction KE between MJO and high-frequency disturbances over the area where the MJO zonal wind is strong. This interaction KE over the MJO convection region is enhanced through its flux convergence and further transport KE to the high-frequency disturbances. This process is conducive to maintaining the MJO convection. This study highlights the importance of KE interaction between the MJO and the high-frequency disturbances in maintaining the MJO convection. [ABSTRACT FROM AUTHOR]

Turbulent energy cascade and intermittency are very important characteristics in the turbulent energy evolution process. However, understanding the temporal–spatial features of kinetic energy transfer and quantifying the correlations between different scales of turbulent energy remains an outstanding challenge. To deeply understand the spatial–temporal features in the energy transfer process, an integrated features identification and extraction method is proposed to quantitatively investigate the correlations using the ocean shear turbulence measured by an autonomous vertical reciprocating profiler (AVRP). The proposed integrated method mainly contains two parallel features analysis modules: first, temporal multiscale features structures of the nonlinear and nonstationary turbulent cascade are identified by Variational Mode Decomposition (VMD); then, the ocean microstructure shear fluctuation data are decomposed into a series of intrinsic mode functions (IMFs), which are characterized by different time scales and frequency bandwidths. The local features of energy transfer are identified when the local intermittency peaks overlap and the phase-synchronization case occurs between two neighboring scales; second, the spatial statistical characteristics of the turbulent energy dissipation are quantitatively studied. The cumulative probability distribution functions (CPDFs) of kinetic energy dissipation are approximated well by a normal distribution, indicating that the turbulent dissipation process exhibits a robust spatial scaling correlation and a few intense dissipation locations dominate the integrated process. Finally, the proposed integrated method is evaluated through experiments using an autonomous vertical reciprocating profiler deployed in the South China Sea. Preliminary experimental results show that the proposed novel method is useful to improve our understanding of turbulent energy transfer and the evolution process in the ocean dynamic systems. [ABSTRACT FROM AUTHOR]

Abstract Fine‐scale motions (

Coastal waters are globally challenging areas to monitor not only because of the high resolution needed to resolve the scales at stake but also because most satellites are not yet suited to near-coast observations. We present here the analysis of an 8-year-long high-frequency RADAR (HFR) dataset off the coasts of Var region (France) in the North-Western Mediterranean Sea. Successive interruptions and errors intrinsic to the nature of the HFR remote-sensing technology have been compensated by the DINEOF statistical filling method. This unprecedented dataset enables the observation of many oceanic processes ranging from the interannual variability of large-scale structures to the identification of (sub)mesoscale features. Comparing and coupling this analysis with outputs from a regional ocean circulation model (GLAZUR), we also put emphasis on the extent of the possibilities of the HFR for the description of coastal surface circulation and its value as part of integrated observation systems. The data showed the diversity of the surface circulation in the region, mainly marked by the Northern boundary Current (NC), but undergoing a great variety of spatial and temporal fluctuations, interannually, seasonally, and at higher frequencies. Strong gusts of wind or regional upstream circulation can cause the undulations of the NC, modifying its shape and its strength, and fostering the emergence and zonal displacement of mesoscale to submesoscale eddies. Using an eddy tracking algorithm, we show that the occurrence of mesoscale eddies off this region display a strong inter-annual variability that is linked to the spatio-temporal variability of the NC's characteristics. The NC system thus plays an intermittent role as a transport carrier or barrier of heat, energy, or matter, which has important consequences for neighbouring coastal areas. [ABSTRACT FROM AUTHOR]

Fine‐scale motions (<100 km) contribute significantly to the exchanges and dissipation of kinetic energy in the upper ocean. However, knowledge of ocean kinetic energy at fine‐scales (in terms of density and transfers) is currently limited due to the lack of sufficient observational data sets at these scales. The sea‐surface height measurements of the upcoming Surface Water and Ocean Topography (SWOT) altimeter mission should provide information on kinetic energy exchanges in the upper ocean down to 10–15 km. Numerical ocean models, able to describe ocean dynamics down to ∼10 km, have been developed in anticipation of the SWOT mission. In this study, we use two state‐of‐the‐art, realistic, North Atlantic simulations, with horizontal resolutions ∼1.5 km, to investigate the distribution and exchanges of kinetic energy at fine‐scales in the open ocean. Our results show that the distribution of kinetic energy at fine‐scales approximately follows the predictions of quasigeostrophic dynamics in summertime but is somewhat consistent with submesoscale fronts‐dominated regimes in wintertime. The kinetic energy spectral fluxes are found to exhibit both inverse and forward cascade over the top 1,000 m, with a maximum inverse cascade close to the average energy‐containing scale. The forward cascade is confined to the ocean surface and shows a strong seasonality, both in magnitude and range of scales affected. Our analysis further indicates that high‐frequency motions (<1 day) play a key role in the forward cascade and that the estimates of the spectral fluxes based on geostrophic velocities fail to capture some quantitative aspects of kinetic energy exchanges across scales. Plain Language Summary: The dynamics of oceanic motions with scales <100 km (fine‐scales) are currently not well known. This is due to the lack of sufficient observational datasets at these scales in the ocean. There are suggestions from recent studies that this class of motions impacts the distribution and exchanges of kinetic energy in the ocean. To better understand fine‐scale motions, the Surface Water and Ocean Topography (SWOT) satellite has been assembled. SWOT is expected for lunch in 2022 and will provide an unprecedented view of the ocean down to a wavelength of 10–15 km. In anticipation of the SWOT mission, numerical ocean models capable of resolving fine‐scale oceanic motions have been designed and implemented. In this study, we use two of these simulations to investigate how kinetic energy is exchanged between oceanic motions at fine‐scales. Our results show that submesoscale turbulence (a class of oceanic turbulence at fine‐scale) and high‐frequency motions affect the kinetic energy exchanges by providing a route to kinetic energy toward dissipation. Also, we found that kinetic energy exchanges based on the future SWOT data set might underestimate the true magnitude of the transfer of kinetic energy toward finer scales. Key Points: We used two submesoscale permitting ocean models of the North Atlantic Ocean to investigate kinetic energy exchanges at fine‐scalesKE fluxes at fine‐scales are strongly impacted by submesoscale turbulence with a stronger forward cascade in winter within the mixed‐layerNot accounting for ageostrophic motions yields a significant underestimation of the forward cascade [ABSTRACT FROM AUTHOR]

Using the local multiscale energy and vorticity analysis (MS-EVA) and based on the global high-resolution ocean reanalysis product GLORYS12V1 for 20 years, this study investigates the energy transfers and conversions of Kuroshio in the Luzon Strait and its adjacent regions through three scales, namely, the climatological scale, the seasonal scale, and the eddy scale. The results show that the inverse cascades of kinetic energy dominate the energy transfer east of Luzon (at both the eddy and seasonal scales). Kuroshio transfers the climatological kinetic energy to the eddy scale through a forward energy cascade in Luzon Strait and east of Taiwan. Because the topography of Luzon Strait and Kuroshio jointly block and limit the westward propagation of non-local eddies, the eddy energy in the South China Sea west of Luzon Strait tends to depend on local forward potential energy cascades. In these subregions, potential energy drives the accumulation of kinetic energy under the action of buoyancy conversion: interannual (seasonal) potential energy as the source of multiscale energy in the Luzon Strait (the east of Taiwan).

In this communication, the closure formulas of von Kármán-Howarth and Corrsin equations are obtained through the Liouville theorem and the hypothesis of homogeneous isotropic incompressible turbulence. Such closures, based on the concept that, in fully developed turbulence, contiguous fluid particles trajectories continuously diverge, are of non-diffusive nature, and express a correlations spatial propagation phenomenon between the several scales which occurs with a propagation speed depending on length scale and velocity standard deviation. These closure formulas coincide with those just obtained in previous works through the finite scale Lyapunov analysis of the fluid act of motion. Here, unlike the other articles, the present study does not use the Lyapunov theory, and provides the closures showing first an exact relationship between the pair spatial correlations calculated with the velocity distribution function and those obtained using the material separation line distribution function. As this analysis does not adopt the Lyapunov theory, this does not need the definition and/or the existence of the Lyapunov exponents. Accordingly, the present proof of the closures results to be more general and rigorous than that presented in the other works, corroborating the previous results. Finally, the conditions of existence of invariants in isotropic turbulence are studied by means of the proposed closures. In the presence of such invariants and self-similarity, the sole evolution of velocity and temperature standard deviations and of the correlation scales is shown to be adequate to fairly describe the isotropic turbulence.

Studies carried out on gust buffeting and aerodynamic admittance show that mode shape represents a sort of watershed. If the mode does not change sign along the structure axis, the problem admits a robust conceptual interpretation based on energy cascade and a simple closed-form solution. If, instead, the mode changes sign, the solution calls for numerical tools, and its physical interpretation definitely is unclear. The companion paper investigated this issue within the novel framework of the enhanced equivalent spectrum technique and derived a closed-form solution of the aerodynamic admittance that can be applied to any mode using quasi-steady theory. This solution is precise and simple for modes with a few changes of sign, but it becomes laborious with increasing mode shape complexity; in addition, it provides a partial conceptual interpretation. Both these limitations were overcome in this paper, in which the application of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and to a simple and general closed-form solution. Analyses were limited here to single modes; multiple arbitrary modes are left for future research, as is the generalization of these concepts to arbitrary influence functions. [ABSTRACT FROM AUTHOR]

The loading and response of structures due to gust buffeting is a dominant topic of wind engineering. One of its crucial aspects is the shape of vibration modes. Although numeric solutions are available for any mode, conceptual interpretations and closed-form solutions mainly are limited to the case in which the sign of the mode does not change along the structural axis. For modes that change sign, it is difficult, if not impossible, to recognize the physical role of the parameters that govern the problem and judge analysis results in qualitative form. This paper addressed this issue in the framework of quasi-steady theory by clarifying the relationship linking aerodynamic admittance with mode shape, showed that any mode may be brought back to a piecewise ensemble of regular modes with constant sign, and used this concept to obtain a closed-form expression for any aerodynamic admittance. This solution is simple for modes with few changes of sign, but becomes laborious as mode complexity increases. In addition, it provides a partial conceptual interpretation. Both of these limits were overcome in the companion paper, in which the use of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and a simple and general closed-form solution. [ABSTRACT FROM AUTHOR]

Based on the round‐trip intelligent sounding system, the structure function and spectrum analysis method were carried out to analyze the scale interactions between the small‐scale gravity wave and turbulence in the middle stratosphere. The result showed that the generation of turbulence was closely related to the Kelvin‐Helmholtz (KH) billows. An upscale energy cascade occurred on the spatial scale of KH billows, while a downscale energy cascade occurred on a larger spatial scale (gravity wave scale), which resulted in the breaking of the gravity wave and generation of turbulence. From the multilevel signal measurement, the obvious interactions between turbulence and gravity can be found. The two‐dimensional turbulence that the inverse energy cascade in 2‐D exists simultaneously with a direct enstrophy cascade to the small scales was found, which is considered to be the first‐hand observation result of relevant height. Key Points: The two‐dimensional turbulence is found with bidirectional energy transmissionKH billows are considered to be an important factor in the excitation of turbulenceConvergence and divergence on different scales cause instability within the wave [ABSTRACT FROM AUTHOR]

Lead halide perovskite, as an emerging semiconductor, provides a fire‐new opportunity for high‐definition display and solid‐state lighting. Earthshaking improvements are implemented in green, red, and near‐infrared perovskite light‐emitting diodes (PeLEDs). However, blue PeLEDs are still far behind in performance, which restricts the development of PeLEDs in practical applications. Herein, a facile energy cascade channel strategy via one‐step self‐organized and controllable 2D/3D perovskite preparation by introducing guanidine hydrobromide (GABr) is developed that greatly improves the efficiency of blue PeLEDs. The 2D/3D perovskite structure boosts the energy cascade to induce energy transfer from the wide into the narrow bandgap domains and inhibit free charge diffusion, which increases the density of electrons and holes, and enhances the radiative recombination. Profiting from this energy cascade channels, the external quantum efficiency of blue PeLEDs, emitting at 492 nm, is considerably enhanced from 1.5% of initial blue device to 8.2%. In addition, device operating stability under ambient conditions is also improved by 2.6‐fold. The one‐step self‐organized 2D/3D hybrid perovskites induced by GABr pave a new and simple route toward high‐performance blue emission PeLEDs. [ABSTRACT FROM AUTHOR]

Submesoscale processes in the upper ocean vary seasonally, in tight correspondence with mixed layer thickness variability. Based on a global high‐resolution MITgcm simulation, seasonal evaluation of strong vorticity and spectral analysis of the kinetic energy in the Kuroshio Extension System show the strongest submesoscales occur in March, implying a lag of about a month behind mixed layer thickness maximum in February. An analysis of spectral energy sources and transfers indicates that the seasonality of the submesoscale energy content is a result of the competition between the conversion of available potential energy into submesoscale kinetic energy via a buoyancy production/vertical buoyancy flux associated with mixed layer instability and nonlinear energy transfers to other scales associated with an energy cascade. The buoyancy production is seasonally in phase with the mixed layer depth, but the transfers of energy across scales makes energizing the reservoir of submesoscale kinetic energy lag behind by a month. Plain Language Summary: Submesoscale processes have spatial and temporal scales of O(1–10) km and O(1) day, linking the meso‐ and micro‐scales. Previous works reveal that mixed layer instability, which has extraction rates scaled with mixed layer depth, releases potential energy for the generation of submesoscale kinetic energy in the upper ocean. However, the seasonality of submesoscale kinetic energy in the Kuroshio Extension System region is determined not only by the potential energy releasing due to the mixed layer instability, but also by the energy transfers between different scales. Key Points: Strongest submesoscales in the Kuroshio Extension System occur in March with a month lag behind mixed layer thickness maximum in FebruaryThe buoyancy production is in phase with the mixed layer depth, but the nonlinear transfers of energy across scales lag a few months behindThe seasonality of the submesoscale energy is a result of the competition between the buoyancy production and nonlinear energy cascade [ABSTRACT FROM AUTHOR]

Turbulent energy cascade and intermittency are very important characteristics in the turbulent energy evolution process. However, understanding the temporal–spatial features of kinetic energy transfer and quantifying the correlations between different scales of turbulent energy remains an outstanding challenge. To deeply understand the spatial–temporal features in the energy transfer process, an integrated features identification and extraction method is proposed to quantitatively investigate the correlations using the ocean shear turbulence measured by an autonomous vertical reciprocating profiler (AVRP). The proposed integrated method mainly contains two parallel features analysis modules: first, temporal multiscale features structures of the nonlinear and nonstationary turbulent cascade are identified by Variational Mode Decomposition (VMD); then, the ocean microstructure shear fluctuation data are decomposed into a series of intrinsic mode functions (IMFs), which are characterized by different time scales and frequency bandwidths. The local features of energy transfer are identified when the local intermittency peaks overlap and the phase-synchronization case occurs between two neighboring scales; second, the spatial statistical characteristics of the turbulent energy dissipation are quantitatively studied. The cumulative probability distribution functions (CPDFs) of kinetic energy dissipation are approximated well by a normal distribution, indicating that the turbulent dissipation process exhibits a robust spatial scaling correlation and a few intense dissipation locations dominate the integrated process. Finally, the proposed integrated method is evaluated through experiments using an autonomous vertical reciprocating profiler deployed in the South China Sea. Preliminary experimental results show that the proposed novel method is useful to improve our understanding of turbulent energy transfer and the evolution process in the ocean dynamic systems.